Thermodynamic properties of solid sodium from quasiharmonic lattice dynamics and molecular dynamics

Quasiharmonic-lattice-dynamics and molecular-dynamics calculations were performed on metallic sodium from the low-temperature region to above melting at several different volumes. A pseudopotential model was used that consisted of a large volume-dependent potential plus a small effective two-body potential. From the molecular-dynamics results for the solid phase, we have constructed the Helmholtz free energy and calculated the thermodynamic properties up to the melting temperature. The anharmonic contributions to the internal energy and pressure are determined directly from molecular dynamics without using thermodynamic perturbation theory. Calculated and experimental values of the zero-pressure volume-temperature curve, isothermal bulk modulus, heat capacity, and Gr\"uneisen parameter are found to be in good agreement. We conclude that the pseudopotential model provides an accurate representation of the potential for energies up to melt; molecular-dynamics simulations accurately represent the classical vibrational contributions to the thermodynamic functions at high temperatures and give a meaningful evaluation of the anharmonicity. The combination of quasiharmonic-lattice-dynamic theory in the quantum regime and molecular dynamics in the classical regime provide a simple and natural representation of the vibrational thermodynamics of a solid.